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Ruthlessbaby · 2019年11月20日

问一道题:NO.PZ2019103001000053

问题如下:

Over the next 12 months, Abram expects a stable yield curve; however, Edgarton expects a steepening yield curve, with short-term yields rising by 1.00% and long-term yields rising by more than 1.00%.

Based on her yield curve forecast, Abram recommends to her supervisor changes to the Fund’s holdings using the following three strategies:

Strategy 1: Sell the 3-year bonds, and use the proceeds to buy 10-year bonds.

Strategy 2: Sell the 5-year bonds, and use the proceeds to buy 30-year MBS with an effective duration of 4.75.

Strategy 3: Sell the 10-year bonds, and buy call options on 10-year government bond futures.

Based on Exhibit 1 and Abram’s interest rate expectations, which of the following strategies is expected to perform best over the next 12 months?

选项:

A.

Strategy 1

B.

Strategy 2

C.

Strategy 3

解释:

B is correct.

In a stable yield curve environment, holding bonds with higher convexity negatively affects portfolio performance. These bonds have lower yields than bonds with lower convexity, all else being equal. The 5-year US Treasury has higher convexity than the negative convexity 30-year MBS bond. So, by selling the 5-year Treasury and purchasing the 30-year MBS, Abram will reduce the portfolio’s convexity and enhance its yield without violating the duration mandate versus the benchmark.

为什么说5年期的债券凸性大于30年期的MBS的凸性?哪里的知识点讲到了?我只记得正常债券的凸性是正凸性,含callable的债券凸性是负凸性,负凸性等价于凸性是负数吗?The 5-year US Treasury has higher convexity than the negative convexity 30-year MBS bond. ?

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发亮_品职助教 · 2019年11月20日

嗨,爱思考的PZer你好:


为什么说5年期的债券凸性大于30年期的MBS的凸性?哪里的知识点讲到了?


MBS和Callable bond呈现负凸性,也就是Negative convexity;

CFA三级固收里面,我们只碰到这两种类型的债券呈现Negative convexity;

所以一般如果要在保持Duration不变的情况下,给Portfolio降低Convexity数据,我们会卖出Convexity较大的普通债券(普通债券的Convexity数据为正数),然后买入Convexity会呈现负数的MBS、或者Callable bond;这样起到了在保持Duration不变的情况下,降低组合的Convexity数据。

如下图讲义:


“负凸性等价于凸性是负数吗?”

是的,算出来的Convexity指标是负数,所以称为负凸性。

所有的普通债券用公式求出来的Convexity数据都为正数;而Callable bond和MBS存在一段区间算出来的Convexity为负数,所以我们称他们表现为负凸性。

Convexity可以用数据直接比大小,所以说普通债券的Convexity数据大于Callable bond/MBS的Convexity数据,也就有了以下解析:

The 5-year US Treasury has higher convexity than the negative convexity 30-year MBS bond. 


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